SOLUTION: A stockbroker has money in three accounts. The interest rates on the three accounts are 7%, 8%, and 9%. If she has twice as much money invested at 8% as she does in 7%, three times

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Question 1147008: A stockbroker has money in three accounts. The interest rates on the three accounts are 7%, 8%, and 9%. If she has twice as much money invested at 8% as she does in 7%, three times as much at 9% as she has at 7%, and the total interest for the year is $200, how much is invested at each rate?
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
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Let x be the amount, in dollars, invested at 7%.


Then the amount invested at 8% is 2x dollars,

and  the amount invested at 9% is 3x dollars.


Then the equation expressing total interest of three accounts is


    0.07x + 0.08(2x) + 0.09*(3x) = 200   dollars.


Simplify


    0.07x + 0.16x + 0.27x = 200

    0.5x = 200

    x    = 200%2F0.5 = 400.


ANSWER.  $400 invested at 7%;  $800 invested at 8%  and  $1200 invested at 9%.


CHECK.  0.07*400 + 0.08*800 + 0.09*1200 = 200 dollars,  which is PRECISELY correct (!)

Solved.